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Counting limit cycles with the help of the renormalization group

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Abstract.

We use the renormalization group to set up an easy algorithm for finding the amplitude equation for an arbitrary two dimensional dynamical system of the Liénard type. This allows us to address the second part of Hilbert’s sixteenth problem, at least in the weak damping limit.

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Authors and Affiliations

  1. Department of Mathematics, South Point High School, Kolkata, India

    D. Das

  2. Department of Physics, Jadavpur University, 700032, Kolkata, India

    D. Banerjee

  3. S.N. Bose National Centre for Basic Sciences, Kolkata, India

    J. K. Bhattacharjee & A. K. Mallik

Authors
  1. D. Das
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  2. D. Banerjee
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  3. J. K. Bhattacharjee
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  4. A. K. Mallik
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Correspondence to D. Banerjee.

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Das, D., Banerjee, D., Bhattacharjee, J. et al. Counting limit cycles with the help of the renormalization group. Eur. Phys. J. D 61, 443–448 (2011). https://doi.org/10.1140/epjd/e2010-00281-6

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  • DOI: https://doi.org/10.1140/epjd/e2010-00281-6

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